Spectral Sequence Constructors in Algebra and Topology.

Intro -- CONTENTS -- PREFACE -- I. MODULES OVER HOPE ALGEBRAS -- 1. Hopf Algebras -- 2. Groups -- 3. Lie Algebras -- 4. Modules -- 5. Homology and Cohomology -- II. CUP PRODUCTS -- 1. Introduction -- 2. Relatively Injective Modules -- 3. Relatively Injective Resolutions -- 4. General Resolutions -- III. SPECTRAL SEQUENCE CONSTRUCTORS -- 1. Introduction -- 2. Comparison of Spectral Sequence Constructors -- 3. Cup Products -- IV. FILTRATIONS ON THE NORMALISED STANDARD COMPLEX -- 1. Introduction -- 2. Comparison of the Filtrations -- 3. Calculation of the E[sub(1)]-term -- 4. Lie Algebras -- 5. The Adams Spectral Sequence -- V. DOUBLE PROJECTIVE RESOLUTIONS -- 1. The Construction -- 2. Calculation of the E[sub(1)]-term -- 3. Cup Products -- VI. PAIR OF RESOLUTIONS -- 1. Introduction -- 2. The Coinduced Resolution -- 3. Cup Products -- VII. REPEATED INJECTIVE RESOLUTIONS -- 1. The Grothendieck Construction -- 2. Repeated Coinduced Resolutions -- VIII. EXPLICIT EQUIVALENCES -- 1. Survey of Spectral Sequence Constructors -- 2. Transformation B → A* -- 3. Transformation C → A* -- 4. Transformation B → C -- IX. ACYCLIC MODELS -- 1. Free Functors -- 2. Chain Complexes -- 3 . Filtered Chain Complexes -- 4. The Uniqueness Theorem -- X. COFREE FUNCTORS -- 1. Free Functors Reformulated -- 2. Cofree Functors -- 3. Right Derived Functors -- 4. Filtered Cochain Complexes -- 5. The Uniqueness Theorem -- XI. LOCAL COEFFICIENTS -- 1. Homology with Local Coefficients -- 2. The Uniqueness Theorem -- 3. Homomorphisms -- XII. THE SPECTRAL SEQUENCE OF A FIBRATION -- 1. Introduction -- 2. The Classifying Space of a Group -- 3. Fibrations -- 4. Calculation of the E[sup(2)]-term -- 5. Other Constructions -- XIII. UNIQUENESS OF THE FIBRATION SPECTRAL SEQUENCE -- 1. The Fibration Spectral Sequence Constructor Axioms -- 2. The E[sup(1)][sub(*0)] Axiom.

3. The Comparison Theorem -- 4. The uniqueness Theorem -- XIV. SHEAF COHOMOLOGY -- 1. Sheaves -- 2. Change of Base -- 3. Sheaf Cohomology -- 4. Locally Constant Sheaves -- 5. The Leray Spectral Sequence -- APPENDIX. LIFTING FUNCTIONS -- REFERENCES -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- P -- Q -- R -- S -- T -- U -- V.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.